A significant challenge in fog computing is task allocation, in which computing tasks are assigned to distributed nodes for processing. This problem is NP-hard and involves multiple conflicting objectives. Although some studies have considered these objectives jointly, effectively balancing them while honoring user preferences remains difficult. In this paper, we consider the effect of marginal utility on achieving multi objective balance under user preferences, and formulate a multi objective task allocation problem for fog computing. We introduce a knee-driven set-based level-based learning optimizer (KSLLSO) to find preferred solutions. The knee-point driven strategy identifies regions with high marginal utility, while the set-based operators and level-based learning strategy efficiently search the discrete decision space. Moreover, a constructive solution generation approach and a capacity-guided allocation strategy allow KSLLSO to exploit problem structure and improve optimization performance. Comprehensive experiments comparing KSLLSO with classical and recent methods demonstrate the effectiveness of the proposed approach.

Surrogate model-assisted evolutionary algorithm (SAEA) has become a generalized method for expensive optimization problems (EOPs) with high-cost evaluations. However, most existing SAEAs retrain surrogate models frequently during evolutionary iterations. Besides, the quality of sample data directly affects model accuracy, leading to difficulties in finding the optimal solution. To address these challenges, this paper introduces the tree-based broad learning system (TBLS) as the surrogate model into SAEA framework, and a TBLS-assisted optimizer with incremental learning (TBLSO-IF) is proposed. First, an incrementable TBLS is constructed for predicting the quality of the solution, and the model is incrementally updated by expanding the layer nodes when the samples increase. And then effectively avoids the high computational costs of retraining models from scratch and significantly improves the update efficiency of surrogate models. Second, an adaptive sample augmentation (ASA) strategy is designed to generate more samples for updating the TBLS using a variational autoencoder (VAE). Experiments on 15 problems in the CEC2017 benchmark functions show that the proposed TBLSO-IF algorithm is more effective and competitive than the other five state-of-the-art SAEA methods.

Social networks built on real or online provide platforms for people to share and update their opinions. Based on the influence maximization problem, the opinion maximization (OM) problem aims to locate a set of initial nodes to achieve the maximum of total positive opinion dissemination in the social network. However, decision-makers prefer to have multiple optimal or near-optimal solutions at hand, which brings up the multimodal OM problem. In this paper, we firstly define the multimodal OM problem, which aims at providing several promising sets of initial nodes at one time. To solve this problem, we propose a genetic algorithm with a dynamic fitness sharing niching method (GADN). In GADN, we take the dynamic fitness sharing method to divide the population dynamically, design a repair strategy to fill the possible gap in sets after crossover, and take a scalable reproduction to assign reproductive opportunities. Finally, a series of experiments are conducted on multiple social networks. The results show that the proposed GADN outperforms other methods on both opinion and active ratio in most cases.